A measuring apparatus is an apparatus to form an image of the interior of a measurement object in non-invasive manner. The measuring apparatus transmits a measurement signal (for example, ultrasonic waves) to the interior of the measurement object from the boundary of the measurement object, and converts a measurement value measured at the boundary into a distribution of physical property value of the interior in accordance with an algorithm based on a physical equation which expresses a propagation phenomenon of the measurement signal. The measurement signal serves as a variable of the physical equation, the physical property values serve as a coefficient and an external force term of the physical equation, and the physical equation is used as an equation expressing a relationship between the measurement signal and the physical property values.
Algorithms for converting a measurement signal into physical property values based on physical equations have been studied as a coefficient identification problem and a boundary value problem in the field of scientific computing. Algorithms actually installed in devices are configured with their conversion accuracy reduced by applying approximation to equations in order to reduce the computation amount to an implementable level. An algorithm in a currently-commercialized product is a method of synthesizing directivities on the basis of an antenna technology, and makes such an approximation that each kind of physical property values of the interior of a measurement object is regarded as uniform. A breast-dedicated system, which is an advanced prototype equipped with a projection mapping algorithm similar to that for CT, also makes such an approximation that the physical property value is regarded as uniform, which means to assume the linearity of a measurement signal.
Moreover, as described in Patent Literature 1, a receive waveform is computed from a transmitted waveform in consideration of the non-uniformity of in-vivo physical property value and in consideration of wave propagation defined by the Helmholtz equation or the like. There is also a method of estimating an in-vivo physical property value by iterating a step of correcting the in-vivo physical property value so that a difference between the measured receive waveform and the calculated receive waveform can be made small.